Galerkin Methods for Even-Order Parabolic Equations in One Space Variable
| Autor: | Miente Bakker |
|---|---|
| Rok vydání: | 1982 |
| Předmět: |
Numerical Analysis
Applied Mathematics finite element method Mathematical analysis Sigma jacobi points faedo-galerkin method Parabolic partial differential equation Quadrature (mathematics) Local convergence Computational Mathematics symbols.namesake Cardinal point even-order parabolic equations symbols Partition (number theory) Jacobi polynomials Galerkin method Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis, 19(3), 571-587 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/0719038 |
| Popis: | For parabolic equations in one space variable with a strongly coercive self-adjoint $2m$th order spatial operator, a $k$th degree Faedo-Galerkin method is developed which has local convergence of order $2(k + 1 - m)$ at the knots for the first $m - 1$ spatial derivatives and, if $k \geqq 2m$, convergence of order $k + 2$ at specific interior nodal points. These nodal points are the zeros of the Jacobi polynomial $P^{m, m}_n(\sigma) (n = k + 1 - 2m)$ shifted to the segments of the partition. All these convergence properties are preserved if suitable quadrature rules are used. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|